By a toric surface we mean a complex 2-dimensional normal toric variety. The classification of smooth toric surfaces up to isomorphism or homeomorphism is well known. In particular, the singular cohomology ring is a complete invariant for the homeomorphism classification of smooth toric surfaces. In this talk, we aims to study the homotopy type of toric surfaces and their classification via the cohomology ring under mild restriction on the singularities.

This is a joint work with Xin Fu and Tseleung So.

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